Magnetism continues to be an important subject, both to provide insights into the understanding of condensed matter and cooperative phenomena and for the development of technologically important materials and devices. Materials may be classified into five categories by their responses to externally applied magnetic fields, i.e., dia-, para-, ferro-, ferri-, and antiferromagnetic substances. The study of magnetic properties in the solid state implies an examination of the interaction between the electrons associated with the metal ions, which are substance-specific. Consequently, these magnetic properties differ greatly in strength. Diamagnetism is a property of all materials and opposes applied magnetic fields, but it is a very weak phenomenon. Paramagnetism, when present in semiconductors, can be stronger than diamagnetism and produces magnetization in the direction of the applied field, and proportional to the applied field. Ferromagnetic and ferrimagnetic effects are very large: They produce magnetizations sometimes orders of magnitude larger than the applied field and, as such, are much larger than either diamagnetic or paramagnetic effects.

Magnetic measurements can be extended to study magnetic structure and electronic properties of materials used in lithium power sources, i.e., the so-called lithium intercalation compounds (LiICs). Because Li ions are nonmagnetic (diamagnetic), they indirectly affect magnetic properties through influence on the cation valence of the 3d iron-transition element. Magnetic properties are determined by the structure of sublattice in the oxide framework, the nature of the metal ions, and the electronic states. In this context, magnetic properties are of particular interest because they are found to be a powerful tool to characterize materials, in particular, when impurities and nanoparticles cannot be detected by classical analysis, i.e., X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, etc. Magnetism is therefore indirectly important to the electrochemical properties of materials as well.

Magnetic measurements are also tools used to check the quality of samples. The estimation and analysis of the spontaneous magnetization can reveal the existence of ferromagnetic (ferrimagnetic) particles in samples. The shape of the temperature dependence of magnetization M(H) is indicative of the origin of the magnetic properties. However, it is necessary to correlate the magnetic susceptibility χ m (T) curves and isothermal M(H) plots for a complete analysis of the electronic properties of materials [1].

One goal of the work carried out in our laboratory is the understanding of the local structure in LiICs using resonance spectroscopy, i.e., Raman scattering, Fourier transform infrared, electron spin resonance, and magnetic measurements. This paper presents the magnetic properties of some LiICs to correlate the structural and electronic properties of oxides used as positive electrode materials in rechargeable lithium-ion batteries. Here, we consider typical materials such as compounds of the α-NaFeO2-type structure, i.e., LiNiO2 and LiFeO2; Li–Mn–O frameworks with the spinel structure, i.e., LiMn2O4 and LiCoMnO4; and the phospho-olivine lattices, i.e., LiFePO4, LiMnPO4, and LiNiPO4. The characterization of the magnetic nanoparticles incorporated in these frameworks is deduced from the magnetic susceptibility and magnetization measurements.

Experimental procedure

Nowadays, most of the magnetic properties are studied by various techniques such as neutron diffractometry, magnetometry, NMR, and electron spin resonance. The two resonance spectroscopies are also useful tools for characterizing the local structure in materials.

The microscopic magnetic structure of materials is most often studied by using neutron scattering techniques, and experiments are performed to measure the structure and excitation for all classes of magnetic materials. More recently, synchrotron sources have been used to study the magnetic scattering. The range of wavelength and energy possessed by thermal moderated neutrons allows us to study not only the nuclear long-range, static nature of solids, but also the dynamics (phonons). Similarly, the neutron’s magnetic moment (S=1/2) can be used as a probe to study the magnetism in solids, allowing unparalleled scrutiny of both the magnetic structures (short- and long-range) and the excitations (magnons) of magnetic materials. Neutron scattering techniques are presently considered as the most powerful probe of magnetic materials. When a material has ferromagnetic ordering, the magnetic lattice is the same as the atom lattice, and no new “Bragg reflections” are created (the intensities of existing Bragg reflections change). For an antiferromagnetic state, however, the magnetic lattice is not the same as the atom lattice, and new, purely magnetic Bragg reflections occur. From the pattern of the magnetic Bragg reflections, the details of the antiferromagnetic ordering structure can be deduced, in the same way that crystal structures are solved from the pattern of the (nonmagnetic) Bragg peaks in XRD and (nuclear) neutron diffraction. Neutron diffraction patterns are currently analyzed using the Rietveld fitting procedure [2].

The use of superconducting quantum interference devices (SQUID) in ultrasensitive magnetic measurement systems may nowadays be considered as a standard technique, to the extent that several companies offer reliable and automated commercial SQUID magnetometers. The SQUID consists of two superconductors separated by thin insulating layers to form two parallel Josephson junctions. The device uses a liquid-helium-cooled amplifier to measure the magnetic moment in the range from 10−7 to 300 emu. The field range is from −5.5 to +5.5 T [3].

Data on the temperature dependence of susceptibility are currently recorded on heating the sample using two modes to determine the magnetic behavior: zero-field cooling (ZFC) and field-cooling (FC). The procedure is based on performing two consecutive magnetization measurements: In ZFC, the sample is first cooled down in the absence of a magnetic field and then measured in an applied magnetic field at increasing temperature, FC is performed in a similar magnetic field at decreasing temperature. The results obtained in this way can exhibit a strong dependence of magnetization. The temperature range in which a magnetic hysteresis appears and the temperature at which a magnetic ordering can be detected should be emphasized.

Magnetic properties of solid-state materials

This section summarizes the general trends of magnetic properties for solid-state materials. In electrical engineering, the magnetic susceptibility is the degree of magnetization of a material, M is the magnetic dipole moment per unit volume in response to a magnetic field H, as

$$\chi _{m} = \frac{{\partial M}} {{\partial H}}{\text{.}}$$

If χ m is positive, the material is called paramagnetic and the magnetic field is strengthened by the presence of the material. If χ m is negative, then the material is diamagnetic and the magnetic field is weakened in the presence of the material. Figure 1 displays the temperature dependence of the magnetic susceptibility of paramagnetic, ferromagnetic, and antiferromagnetic solids [4].

Fig. 1
figure 1

Temperature dependence of the magnetic susceptibility of paramagnetic, ferromagnetic, and antiferromagnetic solids

Paramagnetic materials attract and repel like normal magnets when subjected to a magnetic field. For thermal equilibrium, the magnetization of paramagnets is treated using the Brillouin formalism. Under relatively low magnetic field saturation when the majority of atomic dipoles are not aligned with the field, paramagnetic materials exhibit magnetization according to the well-known Curie–Weiss law, which treats the interaction between spins and molecular field

$$\chi _{m} = \frac{{C_{{\text{p}}} }} {{T + \theta _{{\text{p}}} }}{\text{,}}$$

where C p is the Curie constant. The Weiss constant, θ p, typically accounts for magnetic ordering of the electronic moments below the Curie or Néel temperature for uncorrelated spins (in salts, for instance) θ p=0 (see Fig. 1). For a paramagnet having an effective moment μ eff, the Curie constant is written as

$$C_{{\text{p}}} = \frac{{N_{A} p^{2}_{{{\text{eff}}}} \mu ^{{\text{2}}}_{{\text{B}}} }} {{{\text{3}}k_{{\text{B}}} }}{\text{,}}$$

where N A is the molar concentration of ions and μ B the Bohr magneton (μ B=9.274×10−24 J/T). The effective momentum number p eff is defined as

$$p^{{{\text{theor}}}}_{{{\text{eff}}}} = 2{\left[ {S{\left( {S + 1} \right)}} \right]}^{{1/2}} {\text{,}}$$

where S refers to the electronic spin quantum number. Equation (4) is used in the case of the “quenching” of the orbital angular momentum (L=0 and J=S), which occurs frequently for transition-metal ions from the iron group. Table 1 shows the theoretical magneton numbers for iron group ions. Paramagnetic ions with electronic spin, S (e.g., S=3/2 for d3 ions Mn4+ and Cr4+), are associated with magnetic moments, μ eff=− B S, that align in the presence of static magnetic field H 0.

Table 1 Electron configurations and net spins for transition element cations and effective magneton numbers for iron group ions [5]

When the Curie constant is determined experimentally by fitting the linear χ m −1(T) curve in the paramagnetic domain, one can estimate the experimental value for p eff and then know the electronic configuration of the magnetic ion (in the quenched configuration) using the following equation:

$$p^{{\exp }}_{{{\text{eff}}}} = {\left( {\frac{{3k_{{\text{B}}} C_{{\text{p}}} }} {{N_{A} \mu ^{2}_{{\text{B}}} }}} \right)}^{{1/2}} = 2.84{\sqrt {C_{{\text{p}}} } }{\text{.}}$$

An important class of magnetic materials is that of ferromagnets: iron, nickel, cobalt, and manganese. A ferromagnetic substance possesses a spontaneous magnetic moment even in the absence of an applied magnetic field. The saturation magnetization M S is defined as the spontaneous magnetic moment per unit volume. The Curie point Tc is the temperature above which the spontaneous moment vanishes. For iron, Tc=1,043 K [4].

The antiferromagnetic state is characterized by an ordered, antiparallel arrangement of electron spins. The simplest situation in antiferromagnetism arises when the lattice of paramagnetic ions can be divided into two interpenetrating sublattices. We recognize antiferromagnetism by a well-defined kink in the curve of the magnetic susceptibility vs temperature. This kink determines the Néel temperature, T N. Antiferromagnets are also characterized by a negative value of the Curie temperature. Figure 1 summarizes the temperature dependence of the magnetic susceptibility for paramagnetic, ferromagnetic, and antiferromagnetic solids.

The paramagnetic temperature θ p (also called the Weiss constant) is defined as the intercept of the temperature-axis of the high-temperature asymptote to the χ m 1(T) curve. Depending on the type of antiferromagnetic interactions, θ p could be positive or negative. It should be emphasized that θ p is different than the Néel temperature, T N, which is the temperature at which an antiferromagnetic material becomes paramagnetic—that is, the thermal energy becomes large enough to upset the magnetic ordering within the material. T N corresponds to the cusp in the χ m 1(T) curve.

In metals, the conduction electrons are not spatially localized like electrons in partially filled ionic shells. Thus, the magnetic susceptibility of metals follows the Pauli-type paramagnetism, which is essentially independent on temperature [4]. In contrast, the magnetic susceptibility of localized electrons closely follows inverse temperature dependence due to the thermal agitation of spin moments. The magnetic molar susceptibility of localized moments will exhibit Curie–Weiss behaviors in the absence of strong ferromagnetic, ferrimagnetic, or antiferromagnetic couplings.

Many battery-grade materials are paramagnetic in the discharged or charged state. For example, the positive electrode material LiMn2O4 is a mixed-valence compound containing Mn3+ (d4) and Mn4+ (d3) ions. Although the low-spin (d6) Co3+ ions (nominally diamagnetic) in LiCoO2 have paired d-electrons in the fully discharged state, Li1−x CoO2 contains Co4+ (d5) ions when charged. LiNiO2 contains the paramagnetic S=1/2 ions Ni3+ (d7) in the discharged state.

Magnetic properties of layered oxides

A wide variety of LiICs have been studied which include layered compounds based on the α-NaFeO2-type structure (e.g., LiCoO2, LiNiO2, LiNi0.5Mn0.5O2). The structure–magnetic relationships of sodium and lithium ferrites have been investigated to evaluate detectable ferromagnetic impurities [6, 7]. The α-NaFeO2-type structure is built by alternating layers of trigonally distorted FeO6 and NaO6 octahedra sharing edges. Many LiMO2 (M=Ni, Co, Fe, and Cr) compounds have this typical structure which is suitable for very efficient electrochemical lithium extraction–insertion process. The unit cell is rhombohedral (\({\text{R}}\overline{{\text{3}}} m\) space group). The transition-metal ions M are located in octahedral 3a (000) sites, and oxygen anions are in a cubic close-packing, occupying the 6c (00z, 00z) sites. Li cations reside at Wyckoff 3b (001/2) sites. The transition metal and lithium ions are occupying the alternating (111) planes.


Samples of α-NaFeO2 prepared by hydrothermal treatment of a mixture of α-FeOOH and concentrated NaOH aqueous solution appear as simple antiferromagnets below the Néel temperature T N=11 K. Therefore, they do not include any ferromagnetic clusters such as Fe3O4 or γ-Fe2O3 particles. The temperature dependence of the molar magnetic susceptibility is shown in Fig. 2.

Fig. 2
figure 2

Temperature dependence of the magnetic susceptibility of α-NaFeO2

Fitting with the Curie–Weiss law, one obtains C p=4.17 emu K/mol and θ p=−10 K. The negative θ p value suggests that antiferromagnetic interactions are present in α-NaFeO2. Using Eq. (2), the effective magnetic moment, μ eff, is calculated to be 5.8 μ B, which is very close to a spin-only value of high-spin Fe3+ (5.92 μ B).

The effective magnetic moment of LiFeO2 is affected markedly by the contribution of ferromagnetic impurities, easily saturated at the magnetic fields used in the experiments. Two anomalies have been revealed at 40–50 and 90–280 K. The presence of a ferromagnetic impurity such as LiFe5O8 spinel gives a relatively high μ eff value. The variation of the Néel temperature for various LiFeO2 polymorphs is related to the degree of tetragonal distortion [8].


The difficulty of obtaining stoichiometric LiNiO2 free from the presence of excess Ni ions randomly distributed at predominantly Li sites (3b Wyckoff position) is known. The magnetic properties are extremely sensitive to the Ni2+ ion distribution and should be useful to evaluate the stoichiometry deviation in Li1−x Ni1+x O2. However, the confusion of magnetic properties lies in the quality of the sample. Hirakawa et al. suggested an S=1/2 Ising-type antiferromagnetic triangular lattice in the crystal [9]. Other possibilities, such as ferri-magnetism [10], ferromagnetism [11], a new type of spin-frozen states [12], and spin glass [1316], have been evoked.

Figure 3a shows the temperature dependence of the magnetic susceptibility of Li0.99Ni1.01O2. The insert displays the ZFC and FC low-temperature region. After ZFC, a cusp-like peak is observed at 8 K corresponding to the Néel temperature. On the other hand, the FC susceptibility shows little temperature dependence below T N. Such behavior is that of a typical spin glass. The reciprocal susceptibility (Fig. 3b) follows the Curie–Weiss law above 100 K. The parameters obtained by least-square fitting [Eq. (2)] are C p=0.004 emu K/g and θ p=30 K. The effective Bohr magneton number is p eff=1.77. This value is close to that of Ni3+ ion at low-spin state (S=1/2, p=2[S(S+1)]1/2=1.73). The small deviation of the experimental p eff is due to the presence of Ni2+ ions (S=1, p=2.83) at the 3b sites.

Fig. 3
figure 3

a Temperature dependence of the magnetic susceptibility of Li0.99Ni1.01O2. Insert shows the ZFC and FC low-temperature region. b Reciprocal susceptibility of Li0.99Ni1.01O2

Considering that the total susceptibility of a given material is the sum the susceptibility of the various magnetic cations present in the lattice, the effective momentum number p eff of Li0.99Ni1.01O2 is defined as

$$p_{{{\text{eff}}}} = {\left[ {{\left( {1 - z} \right)}p^{2}_{{{\text{eff}}{\left( {{\text{Ni}}^{{3 + }} } \right)}}} + zp^{2}_{{{\text{eff}}{\left( {{\text{Ni}}^{{2 + }} } \right)}}} } \right]}^{{1/2}} {\text{,}}$$

As magnetic measurements are extremely sensitive to the Ni distribution, Eq. (6) is used to evaluate the stoichiometry deviation in Li1−z Ni1+z O2. From Fig. 3, one determines the quantity z=0.01.

Figure 4 shows the applied magnetic field dependence on the magnetization curves M(H) as a function of the stoichiometric deviation, z, in Li1−z Ni1+z O2. The samples were subjected to ZFC down to 4 K and a magnetic field was applied. These data, recorded at 40 K (paramagnetic phase), show clearly the systematic dependence of the effect of stoichiometric deviation on the magnetic behavior. The magnetization can be divided into an extrinsic component of ferromagnetic clusters which saturate easily under the application of a magnetic field of few hundred Gauss, plus the intrinsic part which remains linear in H up to the largest field investigated. Using the superparamagnetic formalism, the magnetization curves are readily computed from the equation:

$$M = M^{{{\text{clu}}}} + \chi _{{{\text{int}}}} H{\text{,}}$$

where χ int is the intrinsic susceptibility and M clu(T,H) is the self-consistent solution of Eq. (6)

$$M^{{{\text{clu}}}} (T,H) = N\mu _{{{\text{eff}}}} (0)\pounds {\left( {\frac{{n\mu _{{{\text{eff}}}} (0)H}} {{k_{{\text{B}}} T}}} \right)}{\text{.}}$$

£ is the Langevin function, N represents cluster concentration, n is the concentration of ferromagnetic particles per cluster, and μ eff is the magnetic moment associated with one cluster. Here the Langevin function can be used due to the presence of macroscopic spins μ eff(0). Using Eqs. (7) and (8), the fit of the magnetization curve allows us to determine the Ni2+ content in Li1−z Ni1+z O2.

Fig. 4
figure 4

Magnetization M(H) recorded at 40 K vs stoichiometric deviation in Li1−z Ni1+z O2 layered compound

LiNi1y Co y O2

Because isostructural LiCoO2–LiNiO2 solid solutions display better electrochemical cyclability than parent oxide end-members, it is now generally recognized that LiNi0.8Co0.2O2 is a potential next-generation positive electrode material to replace LiCoO2. LiNi1−y Co y O2 compounds with 0≤y≤1 were prepared as polycrystalline nanomaterials (d≈200 nm) following a low-temperature sol-gel method [17]. XRD studies indicate that these materials are single phase for 0.2≤y≤1.0 with an ordered distribution of Li and Ni/Co in the layered structure. Nevertheless, as this technique provides only averaged structural information, it is still possible that, locally, there are some defects, among them disorder, that could affect the electrochemical behaviors of these materials. In fact, through FTIR spectroscopy, we observe for the Li–O band a slight deviation from a linear behavior for high nickel content (y≤0.2), which is attributed to the presence of Ni cations in the octahedral interstices of the predominantly lithium layers (cation mixing). In addition, by means of magnetic measurements, χ m (T) and M(H), we detect in all the samples a ferrimagnetic signal, which gets smaller and smaller as the Co content increases, but indeed reveals the presence of some Ni2+ ions occupying Li+ sites that would lead to the formation of small ferromagnetic islands. From those magnetic measurements, we have estimated the size of nanometric magnetic inhomogenities.

Figure 5a and b show the temperature dependence of the magnetic moment of LiNi1−y Co y O2 for y=0.2 and y=0.3, respectively. The first general observation is that the samples with high Ni content (y≤0.2) show ferrimagnetic behavior with a value of Tc, which quickly decreases from Tc (y=0)∼215 K to Tc (y=0..2)∼65 K as y increases, as seen in the χ m (T) and M(H) curves (Fig. 6). Taking into account that perfectly stoichiometric LiNiO2 is considered to be a frustrated antiferromagnetic compound [18], this ferrimagnetic response would be indicative of the existence of Ni2+ ions occupying Li+ places [18, 19]. These interslab ions would lead to a ferromagnetic ordering of the Ni ions in two adjacent (Ni1−y Co y O2) n slabs and to the formation of small ferromagnetic islands in their surroundings with the concomitant apparent ferrimagnetic behavior.

Fig. 5
figure 5

Temperature of the ZFC and FC molar magnetic susceptibility measured under a field H=50 Oe of LiNi1−y Co y O2 samples for a y=0.2 and b y=0.3. A strong deviation from the paramagnetic behavior is observed at low-temperatures for the y=0.2 sample

Fig. 6
figure 6

ZFC magnetization vs applied magnetic field at T=5, 50, 100, and 300 K for LiNi0.8Co0.2O2

In the samples with intermediate substitutions (0.2<y≤0.4), the magnetic features are different. Partial substitution of Ni3+ by Co3+ suppresses the ferrimagnetic response, reflecting that the addition of Co3+ inhibits the presence of the interlayer Ni2+ ions, and therefore favors a better lamellar structure. The positive Curie–Weiss constant calculated for 100<T<300 K (θ p≈+30 K) shows that the Ni–O–Ni nearest neighbor interactions are still present at intermediate substitution levels. Apart from these general trends, magnetic measurements can also provide an approximation to the size of these magnetic islands. In this context, a blocking temperature, which decreases as the Co content increases, is observed in all the ZFC- and FC-type curves for χ m (T). In the high-field region, at this temperature, it is possible to obtain the magnetic anisotropy, K, from the magnetization measurements vs the magnetic field. To do so, we have to take into account that the magnetization approach to saturation can be fitted to the expression [1]

$$M{\left( H \right)} = M_{{\text{S}}} {\left( {1 - \frac{{a}} {{H}} - \frac{b} {{H^{2} }}} \right)} + cH{\text{,}}$$

where M S is the saturation magnetization and a, b, and c are suitable constants. The second term, cH, is the low-field contribution, which is negligible near the saturation. Two examples of these fits for the LiNi1−y Co y O2 samples with y=0.2 and 0.4 can be seen in Fig. 7a,b, and that the b constant is related to the magnetic anisotropy, K, by the expression [20]

$$b = \beta \frac{{K^{2} }} {{M^{2}_{{\text{S}}} }}{\text{,}}$$

where β is a constant that depends on the type of material.

Fig. 7
figure 7

Size of the ferromagnetic clusters in LiNi1−y Co y O2 samples

Assuming a typical value for the β constant (i.e., β=0.0762 [21]), we can deduce the magnetic anisotropy constant from first magnetization curves from

$$K = {\left( {\frac{{bM^{2}_{{\text{S}}} }} {{0.0762}}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} {\text{.}}$$

Following this procedure, we find that the magnetic anisotropy value, which is 6.5×106 erg/cm3 for the LiNiO2 sample at 200 K, increases upon cobalt doping. Interestingly enough, these values are related to the volume of the magnetic clusters that lead to the blocking temperature in the χ m (T) ZFC- and FC-type curves. In this context, we can assume [1]

$$KV = 25_{{k_{{\text{B}}} }} T_{{\text{B}}} {\text{,}}$$

where V is the volume of the magnetic clusters, k B is the Boltzmann’s constant, and T B is the blocking temperature of each particular sample.

Now, supposing that these magnetic clusters are spherical, we obtain that they would have a mean radii of R=3.5 nm in the case of the LiNiO2 sample, and that their size decreases upon Co-doping, becoming R=1.2 nm in the sample with y=0.2, and being further reduced to 0.5 nm in the samples with y=0.3 and 0.4, as shown in Fig. 7.

Magnetic properties of spinels

The spinel material LiMn2O4 can be cycled at ca. 4 V vs Li+/Li from LiMn2O4 to λ-MnO2 with manganese ions remaining the spinel host lattice throughout. LiMn2O4 spinel has shown interesting magnetic properties [2227]. From the point of view of magnetic interactions, both direct (Mn3+/4+–Mn3+/4+) and superexchange (90° Mn3+/4+–O2−Mn3+/4+) interactions are conceivable between the nearest Mn neighbors. According to Goodenough, only Mn4+–O2−Mn4+ interaction is in ferromagnetic coupling, while all other interactions are in antiferromagnetic coupling [28].


Figure 8 shows the inverse magnetic susceptibility obtained after the lithium extraction from LiMn2O4. Over the temperature range 100–300 K, assuming that only the spin part of the Mn ions contributes to paramagnetic moment, the fit of the Curie–Weiss law is obtained with the following values: θ p=−75 K and C p=3.29 emu K/mol. The θ p value is negative, consistent with the apparent antiferromagnetic ordering below T N=30 K. From the Curie constant, the effective moment is determined to be μ eff=3.70μ B, which is a value smaller than the theoretical spin-only value of 3.87μ B for Mn4+ ion. An increase in the nominal manganese oxidation state from +3.5 to +4 should result in a greater covalence state due to the removal of σ antibonding e g electrons associated with the manganese 3d state. So, λ-MnO2 has a greater covalency in the Li–O–Mn4+ bond than in the Li–O–Mn3.5+ bond.

Fig. 8
figure 8

Inverse ZFC and FC magnetic susceptibility for λ-Li0.08Mn2O4 as a function of temperature in a field of 0.1 T

The abrupt increase of magnetization (insert of Fig. 8) is noticeable with decreasing temperature below 30 K, indicating the presence of a ferromagnetic component. The origin of this ferromagnet could be a small amount of impurity phases, such as ferromagnetic Mn3O4, which is probably produced during the lithium extraction from LiMn2O4. However, the observation of spin-glass behavior at temperatures below the paramagnetic regime in the cubic phases LiMn2O4 and λ-Li0.07MnO2 has been reported by Jang et al. [24]. The existence of frozen spins is consistent with the presence of a significant fraction of spins disordered well below the Néel temperature. The value of the ratio f=θ p/T N=2.5 is indicative of a frustrated antiferromagnet. The geometric frustration inherent in the Mn sublattice, which is comprised of a three-dimensional array of a corner-sharing tetrahedral, has been discussed by Greedan et al. [26].


Figure 9 shows the reciprocal magnetic susceptibility of a LiMn2O4 sample synthesized by wet-chemical technique, i.e., succinic-assisted sol-gel method [29]. In the temperature range 2–300 K, the ZFC and FC curves present complex behaviors including a Curie–Weiss law above 140 K. The extracted Curie–Weiss parameters are θ p=−260 K and C p=4.85 emu K/mol. The negative Weiss constant indicates that antiferromagnetic interactions are dominant over ferromagnetic superexchange interactions in the paramagnetic temperature regime. These are the exchange interaction components across a shared octahedral-site edge in LiMn2O4 [30].

Fig. 9
figure 9

The reciprocal magnetic susceptibility of LiMn2O4 sample synthesis by succinic-assisted sol-gel method

The measured effective magnetic moment is μ eff=4.29μ B. The value p eff=4.29 is close to the theoretical spin-only value p eff=4.38, assuming that only Mn3+ and Mn4+ moments are responsible to the paramagnetic behavior of χ m (T), i.e., for Mn3.5+ valence state (p eff =3.87 and C p=1.87 emu K/mol for Mn4+; p eff=4.90 and C p=3.0 emu K/mol for Mn3+). The magnetization curves display a clear splitting of the ZFC and FC data occurring below the paramagnetic temperature regime. A sharp maximum appears at 20 K in the ZFC magnetization. Jang et al. have reported a spin-glass-like behavior indicating the presence of frozen spins in cubic phases λ-MnO2 and LiMn2O4 [31]. The randomness and frustration necessary for spin-glass-like behavior are explained by the octahedral antiferromagnetic network in the [Mn2]O4 sublattice spinel structure, combined with some magnetic disorder. The disorder due to the presence of a valence distribution in the Mn ions is provoked by competing ferro- and antiferromagnetic exchange interactions. This is believed to be responsible for the complex magnetic structure. Frozen spin was also observed in a neutron diffraction study by Oohara et al. [32]. Magnetic susceptibility measurements were also made on oxygen-deficient spinel LiMn2O4−δ (δ=0–0.1) [33].

LiMn2y Co y O4

Various substitutions of manganese by different transition-metal cations have been investigated to improve their electrochemical properties [29]. The Jahn–Teller distortion associated with a large change in cell volume that occurs in the discharged state of LiMnO4 is avoided with an increasing average oxidation state of manganese ions, n Mn>3.5+. On the basis of charge balance arguments, the substitution of a Mn ion for a dopant cation (e.g., Co, Cr, Ni, Al, Li, Zn, etc.) with charge n + will result in the oxidation of 2(3.5-n) Mn ions with average oxidation states of 3.5 to Mn4+.

Figure 10 shows the temperature dependence of the magnetic susceptibility of LiMn2−y Co y O4 (0≤y≤1) samples. In the low-temperature region, a drastic change in magnetization is observed upon substitution of Co for Mn. In particular, the strong anomaly at T=30 K disappears progressively with the introduction of Co3+ ions in the spinel lattice. This is a consequence of the disappearance of the Mn3+ ions in the [Mn2]O4 sublattice. For LiCoMnO4, Mn4+ is the only paramagnetic species. For the y=1 sample, the curve χ(T) can be represented by a straight line obeying the Curie–Weiss law χ m −1=(Tθ p)/C p in the entire temperature range (5–300 K). The very large negative Weiss temperature θ p=−260 K for LiMnO4 decreases to θ p=−20 K for LiMnCoO4, indicating a weaker antiferromagnetic interaction. Hence, it appears that Mn4+ ions in the [Mn4+Co3+] environment have a stable configuration at low temperature. This observation suggests that the cobalt ions themselves must impart a larger electron spin density through the metal–oxygen–lithium bond in addition to the increasing presence of Mn4+.

Fig. 10
figure 10

Temperature dependence of the reciprocal magnetic susceptibility of Co-substituted LiMn2−y Co y O4 spinels

Magnetic properties of Li-phosphates

Recently, transition metal-based compounds containing compact tetrahedral polyanion structural units have been investigated intensively as potential positive electrode materials for lithium-ion batteries [3436]. They are considered as stable, nontoxic, and friendly environmental materials. These compounds can exhibit various voltage-composition dependencies originating from their different structures.

Phospho-olivine LiFePO4

The LiFePO4 olivine structure belongs to the orthorhombic Pnma space group. It consists of a distorted hexagonal close-packed framework containing Li and Fe in octahedral sites and P in tetrahedral sites. Each Li atom is connected by oxygen atoms to six FeO6 units. The FeO6 units are distorted, reducing the symmetry from O h to C s 2. In C s symmetry, the metal d-orbitals split into 3A′ orbitals at higher energy than the two remaining A″ orbitals, unlike O h symmetry, where two orbitals at higher energy are expected. The Fe magnetic ions are in the divalent Fe2+ state, and occupy only the M 2 site, i.e., the center of the FeO6 octahedron unit, while Li occupies only the M l site. As a consequence, Fe is distributed so as to form FeO6 octahedra isolated from each other in TeOc2 layers perpendicular to the [001] hexagonal direction [37]. In addition, the lattice has a strong two-dimensional character because above a TeOc2 layer comes a second layer, at the vertical of the previous one, to build (100) layers of FeO6 octahedra sharing corners, and mixed layers of LiO6 octahedra and PO4 octahedra.

Figure 11 displays the reciprocal ZFC and FC magnetic susceptibility of LiFePO4 measured at H=1 T. LiFePO4 undergoes an antiferromagnetic transition at T N=52 K, with moments aligned along the [010] axis. The most outstanding property of the χ m −1(T) curve for LiFePO4 lies in the fact that the deviation from the Curie–Weiss law remains small in the range 60–300 K. Values of Curie–Weiss constants deduced from the slope of the isothermal magnetization data (Fig. 11) are C p=4.18 emu K/mol and θ p=−145 K. These data are consistent with the magnetism of lithium iron phosphates where an antiferromagnetic ordering at low temperatures was reported [37]. The negative value of θ p is consistent with the antiferromagnetic coupling known for this compound. The value of the effective moment μ eff=5.77 μ B is in agreement with what is expected for Fe(II) ions. The analysis of the exchange paths has been made by Mays [38].

Fig. 11
figure 11

The temperature dependence of the reciprocal ZFC and FC magnetic susceptibility of LiFePO4 measured at H=1 T

Figure 12 displays the magnetization curves of LiFePO4 in the temperature range 4–300 K. Due to the existence of a ferromagnetic component, the magnetization is not a linear function of the magnetic field. The first consequence is an ambiguity in what is called magnetic susceptibility χ m , because M/H is distinct from dM/dH. Because all the magnetic measurements have been performed on a SQUID magnetometer (and not a Faraday balance), the quantity measured is the magnetization M in an applied magnetic field H, so that we shall use the notation χ m =M/H. The other consequence of the nonlinearity of the magnetization is that the data recorded in the “long-moment” made by the SQUID apparatus are not sufficient to get an understanding of the magnetic susceptibilities, and the full investigation of the magnetization as a function of the magnetic field at different temperatures is needed for this purpose (Fig. 13).

Fig. 12
figure 12

Magnetization of LiFePO4 as a function of the applied field in the temperature range 4–300 K

Fig. 13
figure 13

Plot of the dM/dH slope of the magnetization curves to extract χ m

The inverse of the magnetic susceptibility χ m (T) of LiFePO4 samples synthesized by different sol-gel methods is reported as a function of temperature in Fig. 14. At contrast with prior works, these data give evidence of a ferromagnetic ordering at Curie temperature Tc∼216 K, while we expected the evidence of an antiferromagnetic ordering at 52 K. Below Tc, the magnetic susceptibility is independent of temperature, and thus only depends on a demagnetization factor. Above Tc, the Curie–Weiss law is approximately satisfied with a Curie–Weiss temperature close to Tc. The effective Curie constant, however, is sample-dependent. In addition, the Curie–Weiss law is a mean-field law, and thus, valid only far from Tc. This condition, even at room temperature, is not fulfilled, which precludes any quantitative analysis of the magnetic susceptibility curves in Fig. 14 in this framework. Due to the existence of a large ferromagnetic component, the magnetization is not a linear function of the magnetic field [39].

Fig. 14
figure 14

The inverse of the magnetic susceptibility χ m (T) of LiFePO4 samples synthesized by different sol-gel methods

LiMPO4 olivine-related compounds

Other olivine structures LiMPO4 include compounds with M=Ni, Co, and Mn. The temperature dependence of the inverse magnetic susceptibility measured with a SQUID magnetometer is shown in Fig. 15. All compounds exhibit a Curie–Weiss-type dependence on temperature. The data are consistent with the magnetism of LiFePO4, where antiferromagnetic ordering appears at low temperatures. Linear fits provided the Weiss constants and the effective magnetic moments (Table 2), which can be compared to the theoretical spin-only values in Table 1. The reduced MO6 symmetry has a noticeable effect on the magnetic susceptibility of LiCoPO4. We note that Co2+ is expected to have three unpaired electrons (A′) in C s symmetry, consistent with the experimental data, but only a single unpaired electron (e g ) in O h symmetry [40].

Fig. 15
figure 15

The temperature dependence of the reciprocal magnetic susceptibility χ m (T) of LiMPO4 samples (M=Ni, Co, Mn)

Table 2 The Curie–Weiss constants and the effective magneton number for LiMPO4

The magnetic structures in the ordered phases are both collinear for olivines: in LiMnPO4 the magnetic moments are parallel to the a-axis, while in LiFePO4 and LiCoPO4, to the b-axis. In this case, the orbital angular momentum is not completely quenched, and spin-orbit coupling aligns spins along the b-axis. The distance between magnetic ions is one of the strongest factors affecting the magnetic exchange strength. This distance variation accounts well for the observed transition temperature: The highest T N corresponds to the strongest exchange.

For the LiFePO4 phospho-olivine structure, the magnetic properties give evidence of nano-sized ferromagnetic particles, which can be either strongly magnetic (γ-Fe2O3 clusters) or weakly ferromagnetic (Fe2P clusters), depending on the preparation process. The concentration of magnetic clusters also depends on the preparation process and varies from small concentrations (1.0×10−6 of γ-Fe2O3 per formula), in which case, noncollective behavior is observed, to large concentrations (1.9×10−4 of Fe2P clusters per formula) where the dipolar interaction generates superferromagnetism. Ferromagnetic resonance experiments are also reported and are a probe of the γ-Fe2O3 nanoparticles. An overall understanding of the different properties is achieved within a model of superferromagnetism induced by interacting Fe2P nanoparticles (Ait Salah et al., unpublished).

Li x M2(PO4) x compounds

Among the lithium metal polyphosphate family, the compounds described by formula Li x M 2(PO4) x (M=Fe, V, Mo and x=3, 5, 6, respectively) crystallize with the Nasicon-like structure [41]. Plots of the magnetic susceptibility, as a function of temperature for Fe- and V-containing compounds, are shown in Fig. 16. The calculated Curie temperature value equals θ=−46.7 K for Li3Fe2(PO4)3 and θ p=−0.1 K for Li5V2(PO4)5. The negative Curie temperature indicates an antiferromagnetic behavior of the studied materials at temperatures above their Néel point. For Li3Fe2(PO4)3, the magnetic moment μ eff≈5.90μ B is comparable with the theoretical value of Fe3+ (5.92 μ B). For the Li5V2(PO4)5 sample, one obtains μ eff≈1.56 μ B, while the theoretical value equals 1.55 μ B for V4+ and 1.63 μ B for V3+. Values of the magnetic moment for both studied materials are associated with the most occupied transition metal sites [Fe3+ for Li3Fe2(PO4)3 and V4+ for Li5V2(PO4)5, respectively]. For the Mo compounds, a different behavior is observed. This material behaves as a diamagnetic material (i.e., its susceptibility is negative and temperature-independent) in the whole range of temperature.

Fig. 16
figure 16

The Curie–Weiss plots for a iron and b vanadium vitreous Nasicon-like materials


For LiNi1−y Co y O2 materials prepared by wet chemistry, the magnetic measurements of χ m (T) and M(H) have revealed the presence of small ferromagnetic islands arising from the fact that some Ni2+ ions are occupying Li+ places, which leads to a ferromagnetic ordering of the Ni ions in two adjacent (Ni,CoO2) n slabs. The size of these clusters gets smaller and smaller as the Co content increases from R (y=0)=3.5 nm to R (y=0.4)=0.5 nm.

Magnetic characterization of LiMn2O4 spinel materials shows a spin-glass behavior below the paramagnetic regime (T N<25 K). The magnetic properties are determined by interactions between the Mn ions, which in turn depend on the Mn valence distribution in the [Mn2]O4 framework. The short-range antiferromagnetic order is also investigated in the case of cobalt-substituted spinels, namely, LiMn2y Co y O4.

For LiFePO4 phospho-olivine material, the magnetic properties give evidence of nano-sized ferromagnetic particles, which can be either strongly magnetic (γ-Fe2O3 clusters) or weakly ferromagnetic (Fe2P clusters), depending on the preparation process. The concentration of magnetic clusters also depends on the preparation process and varies from small concentration (1.0×10−6 of γ-Fe2O3 per formula), in which case, noncollective behavior is observed, to large concentrations (1.9×10−4 of Fe2P clusters per formula) where the dipolar interaction generates superferromagnetism. Ferromagnetic resonance experiments are also reported and are a probe of the γ-Fe2O3 nanoparticles. An overall understanding of the different properties is achieved within a model of superferromagnetism, which is induced by interacting Fe2P nanoparticles. The magnetic structure of LiMPO4 phospho-olivine lattices is just that which is predicted by the application of Anderson’s theory of superexchange to M–O–P–O–M linkages.